Calculating accurate conductance across model systems to develop techniques for transport across single-molecular junctions.

The current in a molecular junction is a response property (at weak bias) and requires a non-equilibrium treatment (at finite bias), traditional ab initio methods of quantum chemistry and of ground-state DFT have long been regarded as insufficient. There are many well-known approaches that have been developed in many-body physics from decades of studying this problem for mesoscopic systems, such as quantum dots. Such methods are often so computationally demanding that they can only be applied to simplified Hamiltonians, such as the Anderson model or a Hubbard chain. Thus they are not first-principles and do not produce chemically realistic results, or do so only in an empirical fashion. To fill this gap, a standard approach for performing such calculations within DFT was developed early on and is often referred to as non-equilibrium Green’s function (NEGF). In this model, a ground-state DFT calculation is performed for the system with a bias applied, and then the current through the ground-state KS potential is calculated via the Landauer formalism. The Landauer approach can be derived from non-equilibrium Green’s functions, scattering theory, or Kubo linear response. This generally works well for both metal wires and carbon nanotubes, where conductance is simply the product of the number of open channels times the fundamental unit of conductance. However, in the technologically important area of organic molecules between metal leads, standard model calculations often yield conductances that are one or two orders of magnitude larger than experiment.

We endeavor to further improve and understand the modern methods as well as develop new methods to study the quantum conductance problem.

Publications
[147] Nonexistence of a Taylor expansion in time due to cusps Zeng-hui Yang, Kieron Burke, Phys. Rev. A 88, 042514 (2013). [bibtex] [pdf] [doi]
[138] Accuracy of density functionals for molecular electronics: the Anderson junction Z.-F. Liu, J. P. Bergfield, K. Burke, C. A. Stafford, Phys. Rev. B 85, 155117 (2012). [bibtex] [pdf]
[135] The effect of cusps in time-dependent quantum mechanics Zeng-hui Yang, Neepa T. Maitra, Kieron Burke, Phys. Rev. Lett. 108, 063003 (2012). [bibtex] [pdf] [doi]
[132] Bethe Ansatz approach to the Kondo effect within density-functional theory J. P. Bergfield, Z.-F. Liu, Kieron Burke, C. A. Stafford, Phys. Rev. Lett. 108, 066801 (2012). [bibtex] [pdf]
[103] Density functional calculations of nanoscale conductance Max Koentopp, Connie Chang, Kieron Burke, Roberto Car, Journal of Physics: Condensed Matter 20, 083203 (2008). [bibtex] [pdf]
[101] Pride, Prejudice, and Penury of ab initio transport calculations for single molecules Ferdinand Evers, Kieron Burke, Chapter in Nano and Molecular Electronics Handbook 24-1 (2007). [bibtex] [pdf]
[94] Self-Interaction Errors in Density-Functional Calculations of Electronic Transport C. Toher, A. Filippetti, S. Sanvito, Kieron Burke, Phys. Rev. Lett. 95, 146402 (2005). [bibtex] [pdf] [doi]
[92] Kohn-Sham master equation approach to transport through single molecules Ralph Gebauer, Kieron Burke, Roberto Car, Chapter in Lecture Notes in Physics 706, 463 (2006). [bibtex] [pdf] [doi]
[88] Coordinate scaling in time-dependent current-density-functional theory Maxime Dion, Kieron Burke, Phys. Rev. A 72, 020502 (2005). [bibtex] [pdf] [doi]
[87] Zero-bias molecular electronics: Exchange-correlation corrections to Landauer\textquoterights formula Max Koentopp, Kieron Burke, Ferdinand Evers, Phys. Rev. B 73, 121403 (2006). [bibtex] [pdf] [doi]
[85] Density Functional Theory of the Electrical Conductivity of Molecular Devices Kieron Burke, Roberto Car, Ralph Gebauer, Phys. Rev. Lett. 94, 146803 (2005). [bibtex] [pdf] [doi]
[69] Current-density functional theory of the response of solids Neepa T. Maitra, Ivo Souza, Kieron Burke, Phys. Rev. B 68, 045109 (2003). [bibtex] [pdf] [doi]

Funding
We graciously acknowledge support from the Department of Energy (DE-FG02-08ER46496).

Current Student

Justin Smith

Alumni

Zhenfei Liu

Senior Collaborator

Roberto Car